You could first do the analysis on a different level, eg protein level (plenty of tools to do this: MCscan, i-ADHORE, ... ) and once you pinpointed potential interesting regions look into detail on the nucleotide level ?

while minimap2 is likely still the best go-to option, it is very well possible you need to tweak the parameters little to get it to finish. Did you use default settings? consider increasing the kmer size and/or window size.

Wheat genomes are notoriously repetitive rich so it is not surprising they cause issue with memory and such (on top of the near 1gb chromo size, which is an issue itself already)

I agree that starting with something like a orthology based approach to see if similar genes are on similar chromosomes might be a simpler approach.

Another suggestion would be to mask repetitive regions in both genomes for the analysis. I suspect this is what's driving the memory use so high. But this really depends on the research questions of your study.

Final suggestions is to limit your query sequence to just a single chromosome/contig. As long as your target input is the entire genome it should be fine to just concatenate the results into a single file.